It takes 15 machines 15 minutes to make 500 raviolis. The machines produce raviolis at a steady rate. How long would it take 75 of these to make 6000 raviolis?
time is inversely proportional to the number of machines and directly proportional to the number of raviolis
t = 15 min * 15/75 * 6000/500
or
15 machines 15 minutes to make 500 raviolis
75 machines 15 minutes to make 2500 raviolis
75 machines 15(2.4) minutes to make 2500(2.4) raviolis
75 machines 36 minutes to make 6000 raviolis
(the 2.4 comes from 6000/2500)
To find the time it would take for 75 machines to make 6000 raviolis, we can use the concept of proportion.
First, let's find out how many raviolis one machine can produce in 15 minutes. We divide 500 (the number of raviolis) by 15 (the time in minutes) to get the rate per machine: 500 / 15 = 33.33 raviolis per minute (rounded to two decimal places).
Since we want to calculate the time it takes for 75 machines, we multiply the rate per machine by the number of machines: 33.33 * 75 = 2499.75 raviolis per minute.
Next, we set up a proportion with the given rate and time to solve for the unknown time:
(2499.75 raviolis) / x minutes = 6000 raviolis / 1 minute.
To solve for x, we cross-multiply and divide: x = (2499.75 * 1) / 6000 = 0.4166 minutes.
Therefore, it would take approximately 0.4166 minutes for 75 machines to make 6000 raviolis.